M03-24

Question

If  n  is a positive integer, is  n^x  an even integer?

(1)  n  is an even integer
 
(2)  x^2-3x+2 = 0

Bunuel · Accepted Answer

Official Solution:

If  n  is a positive integer, is  n^x  an even integer? 
 
(1)  n  is an even integer. 
 
If  x=0 , then  n^x=1=	ext{odd} . However, if  x=1 , then  n^x=n=	ext{even} . This statement alone is not sufficient to determine if  n^x  is even.
 
(2)  x^2-3x+2 = 0 . 
 
Either  x=1  or  x=2 . This statement alone is not sufficient, since it provides no information about  n .
 
(1)+(2) Given that  n=	ext{even} , then both  n^1  and  n^2  will be even. Sufficient.

Answer: C

minwoswoh · Answer

This question shows how important it is to sometimes restate the question in our own words before diving into the statements (not too far away from the Prethinking in Critical Reasoning, huh?)

Question Stem "Prethinking"  
For the expression to be an even number, we need 2 things:
I) n must be an even number
II) x must be integer and positive.

Statement 1: addresses I but doesn´t address II --> Not Sufficient
Statement 2: Factor the quadratic and you´ll get (x - 1)(x - 2) = 0. Therefore, x = 1 or x = 2. This addresses II but doesn´t address I --> Not Sufficient
(1) + (2): both conditions are addressed --> Sufficient.

akhilshrmaa · Answer

For n^x to be even
1-> n has to be even number
2--> x needs to b a positive integer.

Statement 1 gives us the first condition but does not tell about the value of.
Statement 2 gives us x=1 or 2 which gives us the second conditions but does not tell us about the value of n.

So by combining both statements we have both required conditions fulfilled.
Hence Answer-C

Kudos

healthjunkie · Answer

This question sparked something for me.. can fractions be considered even or odd? For example in statement 1 what if x were negative? So lets say n=4 and x=-2. I assume we don't consider 1/16 to be even since when divided by 2 it does not produce an integer?

Thanks!

Thanks!

Bunuel · Answer

1. An even number is an integer that is "evenly divisible" by 2, i.e., divisible by 2 without a remainder. Even integers are: ..., -6, -4, -2, 0, 2, 4, 6, 8, ... 2. An odd number is an integer that is not evenly divisible by 2: ..., -5, -3, -1, 1, 3, 5, ... Theory on Number Properties: math-number-theory-88376.html Tips on Number Properties: number-properties-tips-and-hints-174996.html All DS Number Properties Problems to practice: search.php?search_id=tag&tag_id=38 All PS Number Properties Problems to practice: search.php?search_id=tag&tag_id=59

nshivapu · Answer

It is given that (in the question stem) n is a positive integer, that means n>0
Now, if S1 specifies that, n is also even, that means n>1
Thus, eg: 2^x where x irrespective of being odd or even is still going to leave n^x as even

On solving S2 we get S as either 1 or 2. Thus, insufficient

And, I arrived at answer as A

Kindly let me know how do I guard against such ambiguity, of what is specified in the question stem vs the Statements. I mean should I consider statements independent of the question stems or Should question stems stand as true come what may.

Thanks, Pls correct me if I am wrong.

Bunuel · Answer

On the GMAT, two data sufficiency statements always provide TRUE information and these statements never contradict each other or the stem.  
_________________

In this question notice that the stem says that n is a positive integer and then (1) says that it's even, so n could be 2, 4, 6, 8, ... Notice also, that neither the stem nor the first statement says anything about x. It could be even or odd, it could be a fraction, or an irrational number.

If x is a positive integer, then n^x = (positive even integer)^(positive integer) = even. But if say x is a fraction, then n^x won't necessarily be even, for example, if n = 2 and x = 1/2, then  n^x=\sqrt{2} , which is not an integer, hence is not even. Or consider example given in the solution:  x=0  then  n^x=1=	ext{odd} . So, from (1) n^x could be even, odd or not an integer at all, which means that (1) is NOT sufficient.

Does this make sense?

19PRASHANT95 · Answer

nice

Bunuel · Answer

I have edited the question and the solution by adding more details to enhance its clarity. I hope it is now easier to understand.

BottomJee · Answer

I think this is a  high-quality  question and I agree with explanation.

M03-24

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